To further improve the efficiency of proximal algorithms,
proximal operators based on generalized Bregman distances have
been proposed and incorporated in many methods
[1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}.
Bregman distances offer two potential benefits.
First, the Bregman distance can help build a more accurate local
optimization model around the current iterate.
This is often interpreted as a form of preconditioning. For example,
diagonal or quadratic preconditioning [10]}, [11]}, [12]}
has been shown to improve the convergence rate of PDHG,
as well as the accuracy of the computed solution [13]}.
As a second benefit, a Bregman proximal operator of a
function may be easier to compute than
the standard Euclidean proximal operator, and therefore
reduce the complexity per iteration of an optimization algorithm.
Recent applications of this kind include optimal transport
problems [14]}, optimization over nonnegative trigonometric
polynomials [15]},
and sparse semidefinite programming [16]}.
